Calculus Questions

Find the solution of the simultaneous linear differential equations dx dt dy 2x2y 4e 2t dt that satisfies the initial conditions 0 7 y 0 4 5x 3y 17e 2t

Suppose that f is the function given in the graph below and that f is a piecewise function whose parts are either portions of lines or portions of circles as pictured 6 3 4 3 A 6 2 A 1 1 6 5 4 3 2 1 2 3 5 6 Let A be the function defined by A 2x f t dt b Compute the followings 5 q a What does the Second FTC tell us about the relationship between A and f Write an equation to describe the relationship 0 1 pt 30 29

roblem 3 Evaluate the following integral Problem 3 3 6 cot x In sin x dx Enter yo as in the

Problem 6 Find the arc length of the following function on the given interval f x 4 24 1 4x n 1 x 2 Enter your answer as an exact fraction or as a number correct to 4 decimals

Problem 7 Find an expression for the arc length of the upper half of a circle of radius 22 on the interval 0 t where 0 t 22 Problem 7 Enter your answer as a symbolic function of t as in these

roblem 1 Evaluate the following integral 4 x 2 x 5 dx Don t forget the absolute value in your answer Problem 1 Enter your answer as a symbolic function of x as in these examples Don t forget the absolute in your answer Use abs for absolute v

Problem 5 Evaluate the following integral 3 8 1 So 64x 9dx 0

Problem 4 Evaluate the following integral 1 2 100 Problem 4 dx Enter your answer as a sym function of x as in these examples

Problem 6 Consider the partial fraction decomposition of the following Problem 6 1 x 1 x 8 One of the terms in the partial fraction decomposition is of the form Enter your answer symbolically as in these examples B x 8 Find the value of B

Problem 4 By making an appropriate substitution which of the following integrals is equal to SFR Problem 4 dx x x 9 5 2 8 A 37 sin 8 G Select de B 37 sin e cos 8 38 sin 8 de H de c f cos 8 37 sinf 8 de cos 0 37 sin 0 de D 38 sin 6 de E S de F cos 0 37 sin 8 cos 8 38 sin 8 S

Problem 1 Evaluate the following integral S 12 sin 6x dx

Problem 3 Evaluate the following integral dx 1 x 16 A j 7 16 is arctan C B 16 Tarctan f C 2 16 arctan C 2 2 D 16 1 6 arctan C E 16 1 arctan C F 16 arctan C 16 16 arctan C H 216 arctan C G Problem 3 Select

Problem 2 By making an appropriate substitution which of the following integrals is equal to tan x sec 0 x dx Problem 2 A u 1 u du B x 1 u du C us 1 u 6 du D u 1 u du E u 1 u du F u 1 u 4 du G u 1 u 5 du H u 1 u du hs Select

Problem 5 Find the remainder after performing the following divis 11x 5x x 5 Problem 5

A rectangle is inscribed with its base on the x axis and its upper corners on the parabola y 5 x What are the dimensions of such a rectangle with the greatest possible area Width Height 15 3 10 3

The data in the table below represents the percentage of patients who have survived after diagnosis of advanced stage breast cancer at 6 month intervals of time Time after Diagnosis years 0 5 1 1 5 2 2 5 3 3 5 Percentage Surviving 95 8 83 4 74 0 58 7 46 6 40 9 32 2 a Using a graphing utility build an exponential model from the data y 120 5681 0 6918 Type integers or decimals rounded to four decimal places as needed b Express the function found in part a in the form A t Aet where t x A t Type integers or decimals rounded to four decimal places as needed

Let u 5 4 and v 4 6 Find the a component form and b magnitude length of the vector 5 12 13 13 a 5 13 12 13 V

K 5 9 A strain of bacteria is placed into a petri dish at 30 C and allowed to grow The following data are collected Theory states that the number of bacteria in the petri dish will initially grow according to the law of uninhibited growth The population is measured using an optical device in which the amount of light that passes through the petri dish is measured Complete parts a e Time hours x 0 25 3 5 4 5 6 HO Population y 0 27 0 53 0 76 1 03 1 46 A strain of bacteria is placed into a petri dish at 30 C and allowed to grow The following data are collected Theory states that the number of bacteria in the petri dish will initially grow according to the law of uninhibited growth The population is measured using an optical device in which the amount of light that passes through the petri dish is measured Complete parts a e Time hours x 0 2 5 35 45 6 Population y 0 27 0 53 0 76 1 03 1 46 CCC a Treating time x as the predictor variable use a graphing utility to fit an exponential function to the data yab 0 2698 1 3328 Round to four decimal places as needed b Express the function found in part a in the form N t Noe where x t N t 0 26980 28731 Round to four decimal places as needed c Graph the data together with the exponential function found in part a or part b on a scatter diagram Which graph correctly illustrates the exponential model found for this data Question 1 5 9 1 GC Part 4 of 5 Q NEUV ZUBOE Round to four decimal places as needed c Graph the data together with the exponential function found in part a or part b on a scatter diagram Which graph correctly illustrates the exponential model found for this data G 200 G i C E HW Score 8 33 1 of 12 points Points 1 of 5 d Use the exponential function from part a or b to predict the population at x 7 hours 0

If AB i 5j 4k and B is the point 9 4 1 find A

The financial director of a hotel finds that the income stream measured in thousands of dollars varies depending on the season She estimates that the total income can be modeled using the continuous distribution f t t 361 288t where t is measured in months What is the total income in the first year Give your answer in thousands of dollars to the nearest thousand dollars Provide your answer below

A company models its income in thousands of dollars using the conti f t 20e 0 0251 12 where t is measured in months Which of the following denotes the correct formula to find the total income derived in the second year Select the correct answer below 24 O TI 20e 0 0251 1 2 dt 12 TI 2 20e 0 025r 2 dr 20e 0 025t dt O TI 36 O TI 2 20e 0 025z 2 dt O

A strain of bacteria is placed into a petri dish at 30 C and allowed to grow The following data are collected Theory states that the number of bacteria in the petri dish will initially grow according to the law of uninhibited growth The population is measured using an optical device in which the amount of light that passes through the petri dish is measured Complete parts a e Time hours x 0 2 5 3 5 4 5 6 Population y 0 27 0 53 0 76 1 03 1 46 a fialny w a as the pituition and the a graping unity to in an OAUTOT CE to o to y ab 0 2698 1 3328 Round to four decimal places as needed b Express the function found in part a in the form N t Noekt where x t N t 0 2698e0 2873t Round to four decimal places as needed c Graph the data together with the exponential function found in part a or part b on a scatter diagram Which graph correctly illustrates the exponential model found for this data A OB O C 1 2 0 2 0 2 Q Q Q Q Q

What is the value of the definite integral exact fraction if necessary Provide your answer below 3 1 2 21 1 2 di Enter your answer as an

Let A z f t dt with f x shown in the graph below 0 st 4 3 2 1 2 3 At what x values does A x have a local max x At what x values does A x have a local min x Restrict your answers to values 0 x 6

If q r S d r cost t2 cos 5 0 2r dt then syntax error Question Help Video Add Work X

Let f x 5e 2 3 3 1 1 6 de t dt 0 1 List all values of x for which f x has a local maximum X

Given At what value of x does the local max of f x occur x f x S a At what value of a does the local min of f x occur x t 5t 24 1 cos t dt

If q r d r cost9 t2 cos r 2r F Quoction Hair mucu dt then X

26 If y x 8 widw then 0 y x 6x6 8 x 4 24 Question Help Video X

If q r Syr d r cost9 t dt then

If y x 1 V8 widw then

4 I If h x h x 5 0 84 dw COS dw then

If f t n s 49 7 ds then f t 1 8

Find the derivative of y with respect to x t or 0 as appropriate In x x6 27 y A 1 6ln x x12 B 6ln x 1 x7 1 6In x x7 D 1 6lnx x12

Next question 17 If f x t Get a similar question You can retry this to dt then f x 17 Hint Remember that f a t d 1 to to dt 17 Find the derivative of g a sin 1 dt g x sin x

Answer the following questions about F x x 43x 486 B Graph F x and use geometric formulas to calculate the area between the graph of F x and the x axis from x 10 and x 15 Choose the correct graph below 20 10 15 OB 60 40 20 10 20 OC 20 10 10 20 Q OD 1000 500 50 100

ind the derivative of the function 25 r sec 0 tan 0 2 A 2 sec 0 tan 0 3 tan2 0 sec 0 tan 0 C 2 sec 0 sec 0 tan 0 2 B 2 sec 0 tan 0 sec 0 D 2 sec 0 tan 0 3

Use geometric formulas to find the unsigned area between the graph of y f x and the x axis over the indicated interval f x x 8 2 9 The area between f x and the x axis is Type an exact answer using a as needed

1 6 Find the area y 3x 15 and y x 5 and the y axis x20 LOW

Find the critical point s of the function f x y y6 6xy 12x and determine whether each is a local maximum local minimum a saddle point or none of these Enter the critical point s as point s a b Number of critical point s Choose one

Current Attempt For f x y A x Bx y Cy what values of A B and C give f x y a local maximum value of 17 at the point 6 7 A B C i

Find an equation for the tangent to the curve at the given point 20 f x 8 x x 9 64 9 A y x 9 B y 9 C y x 41 1 D y x

For f x y A x Bx y Cy what values of A B and C give f x y a local maximum value of 17 at the point 10 2 A B C i i Bul i

T 1 A graphing calculator is recommended Sketch the region enclosed by the given curves 1 x3 y y 1 x2 0 5 0 5 y 1 0 0 5 0 5 1 0 y 1 0 0 5 0 5 0 5 0 5 1 0 1 0 M 0 5 0 5 al y 1 0 0 5 y 1 0F 0 5 1 0 0 5 0 5 JS Secti 0 5 0 5 1 0 1 5 1 0 2 0

etermine where the given function is concave up and where it is concave dow 19 f x 4x x3 A Concave up on 0 concave down on 0 B Concave up on 0 and 1 concave down on 0 1 C Concave up on 0 concave down on 0 D Concave down for all t

T S S Sketch the region enclosed by the given curves y 3 x y 12x Y 3 6 1 y 8 2 X 0 3 4 82 M 6 th y 8 JS Secti MacBook Air 2 dh 3

Find the extreme values of the function and where they occur 17 y 1 x2 1 A None B Local maximum at 0 1 C Local maximum at 1 0 local minimum at 1 0 D Local maximum at 1 0 local minimum at 1 0

y 3 M al JS Secti al ah Sketch the region enclosed by the given curves Decide whether to integrate with respect to x or y Draw a typical approximating rectangle y ex y x 1 x 1 x 1 y 3 5 2 0 webassign net y 3 y MacBook Air

Find the area of the shaded region y 3 2 1 1 1 5 10 y x y XIT 15 20 X 27 25 PERM X

Atte Sketch the region enclosed by the given curves x 9y2 x 2 7y 1 0 y 0 5 0 5 1 0 1 0 0 0 5 0 5 8 1 0 M 1 0 0 5 0 5 y 1 0 1 0 0 5 webassign net JS Secti y 8 MacBook Air 6 8 0 5 1 0 X